(106e) Nonlinear Reactor Design Optimization with Embedded Microkinetic Model Information for Sustainable Shale Gas Processing

The 2015 Paris Agreement ^[1] goal of limiting global warming to well below 2°C and pursuing efforts to limit it to 1.5°C above pre-industrial levels necessitates re-thinking and adaptation of current energy systems. Such a goal demands a sustainable use of energy resources to reduce greenhouse gas (GHG) emissions while satisfying the energy demand. The US shale gas sector has expanded its production in recent years and as a result, dry natural gas (NG) and natural gas liquids (NGL) production has surged notoriously. The efficient and strategic utilization of shale gas is, therefore, crucial for the energy transition towards net-zero emission. The combination of process development along with environmental assessment can provide crucial guidance during the conceptual development stages of novel, modular ^[2], catalytic processes ^[3] for sustainable shale gas transformation. Multiscale modeling plays a critical role in modernizing the energy economy including the responsible use of shale gas; the incorporation of detailed kinetic information in process design facilitates confident and meaningful product portfolio estimations. However, a key challenge in multiscale modeling is determining the appropriate, fit-for-application scale-bridging strategy. On the other hand, adding environmental impact metrics capable of observing GHG emissions from different process configurations, operating conditions, and design thresholds facilitates the selection of sustainable processing schemes; state-of-the-art processes have studied the feasibility of producing liquid fuels from different shale gas feedstocks ^{[3, 4, 5]} including its associated environmental impacts ^[6]. However, not much attention has been focused on studying the effect of GHG emissions constraints on process design. As part of the NSF-funded Center for Innovative and Strategic Transformation of Alkane Resources (CISTAR), we are developing computationally tractable scale-bridging approaches to incorporate information from multi-product microkinetic (MK) models ^[7]with thousands of rates and chemical species into nonlinear reactor and process optimization problems to facilitate the design of sustainable shale gas processing systems.

Although MK models of catalytic processes help elucidate reaction phenomena such as catalyst-reactant interactions, catalyst lifespan, and final product distributions, they are seldom utilized in the design, optimization, and scale-up of industrial reactors due to their numerical tractability concerns ^{[8, 9, 10]}. Engineers often use conversion or equilibrium models (e.g., Gibbs free energy minimization) for process design and optimization ^[3]. For complex reaction networks such as oligomerization in natural gas upgrading, the use of such simplified models may lead to inaccurate conclusions by not considering chemical kinetics. MK model reduction strategies have received considerable attention in recent literature ^{[8, 9, 10]} and have been used to demonstrate model size reductions of up to 50% for small reaction networks, i.e., O(10) elementary reaction steps, but, are yet to be demonstrated on complex reaction networks such as oligomerization which consider O(1000) elementary reaction steps ^[7] and multiple products. On the other hand, machine learning approaches ^{[11, 12]} use reaction data to train surrogate models and are not restricted by the MK model size but, require large amounts of data to train and lack reliability outside validation range. In contrast to these approaches, reduced-order kinetic (ROK) models ^[13] are developed by lumping the MK reactant and product species into major products or product groups following simplified reaction mechanisms to reduce complexity. These models are computationally tractable due to the reduced model size while the kinetic form of the models enables considerably reliable process-scale extrapolations. This makes ROK models especially attractive for multiscale oligomerization reactor optimization.

In this work, we demonstrate reduced-order kinetic (ROK) modeling approaches for catalytic oligomerization in shale gas processing. Specifically, we answer the following questions: (a) what ROK model-form best emulates MK simulation data while remaining computationally tractable for dynamic optimization? and (b) what is the impact of ROK model-form and parametric uncertainties on reactor design optimization results? We assemble a library of six candidate ROK models based on literature. We find that three metrics - quality of fit, thermodynamic consistency, and model identifiability - are all necessary to train and select ROK models. Using a subset of the best ROK models, we optimize the temperature profiles in staged packed bed reactors to maximize conversions to heavier oligomerization products. We find that optimal temperature profiles are qualitatively consistent at feed space velocities corresponding with laboratory-scale to well-scale operation. Through first-order uncertainty propagation using the calibrated parameter covariance matrix of the ROK models, we find that parametric uncertainty induces less than a 10% deviation in the reactor optimization objective function. In contrast, we find the ROK model choice leads to a 22% difference in the objective function values. This highlights the importance of quantifying model-form uncertainty, in addition to parametric uncertainty, in multiscale reactor and process design and optimization. Additionally, the fast dynamic optimization solution times (under 15 CPU seconds using Pyomo, IPOPT, and HSL) suggest that the ROK strategy is suitable for incorporating complex molecular information in sequential modular or equation-oriented process simulation and optimization frameworks.

As ongoing work, we are using this multiscale modeling framework to tractably incorporate microkinetic detail ^[7] in process design using validated ROK models combined with a tailor-made emissions assessment tool. We embed the multiscale model in the shale gas upgrading process design ^[3] using the equation-oriented framework IDAES ^[14]. The IDAES modeling library facilitates simultaneous process optimization, which helps to recognize optimal design decisions that remain unrealized when using conventional sequential process simulation tools. This framework will be capable of handling uncertainty and sensitivity analyses as well as process optimization considering yields, process configurations, and GHG emissions simultaneously.

References

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[14] Lee, A., Ghouse, J. H., Eslick, J. C., Laird, C. D., Siirola, J. D., Zamarripa, M. A., ... & Miller, D. C. (2021). The IDAES process modeling framework and model library—Flexibility for process simulation and optimization. Journal of Advanced Manufacturing and Processing, 3(3), e10095.